Complete Guide to Perimeter of Regular Polygon Formula for 3rd Grade

Master calculating perimeter of regular polygons including rectangles, squares, triangles, pentagons, and hexagons with detailed exercises and solutions.

Regular Polygon Formula Solutions
1 Rectangle perimeter
Exercise 1
A rectangle has a length of 8 cm and a width of 5 cm. What is its perimeter?
Definition:

Regular Rectangle: A 4-sided shape with opposite sides equal. P = 2 × (length + width)

Method:
  1. Write the perimeter formula for a rectangle
  2. Substitute known values
  3. Calculate the result
  4. Include the unit
Given
l = 8, w = 5
Formula
P = 2(l+w)
Calculate
P = 26 cm
Step 1: Write the perimeter formula

For a rectangle: Perimeter = 2 × (length + width)

P = 2(l + w)

Step 2: Substitute known values

P = 2(8 + 5)

Step 3: Calculate

P = 2(13) = 26

Step 4: Include unit

The perimeter is 26 cm.

Perimeter = 26 cm
Final answer:

The perimeter of the rectangle is 26 cm.

Applied rules:

• Rectangle perimeter formula: P = 2(l + w)

• Addition: Add length and width first

• Multiplication: Multiply by 2

2 Square perimeter
Exercise 2
A square has sides of 7 cm. What is its perimeter?
Definition:

Regular Square: A 4-sided shape with all sides equal. P = 4 × side length

Given
side = 7 cm
Formula
P = 4s
Calculate
P = 28 cm
Step 1: Write the perimeter formula for a square

For a square: Perimeter = 4 × side length

P = 4s

Step 2: Substitute the side length

P = 4(7)

Step 3: Calculate

P = 28

Step 4: Include unit

The perimeter is 28 cm.

Perimeter = 28 cm
Final answer:

The perimeter of the square is 28 cm.

Applied rules:

• Square perimeter formula: P = 4s

• All sides equal: In a square, all four sides are the same length

• Multiplication: Multiply side length by 4

3 Triangle perimeter
Exercise 3
An equilateral triangle has sides of 6 cm. What is its perimeter?
Definition:

Regular Triangle (Equilateral): A 3-sided shape with all sides equal. P = 3 × side length

Given
side = 6 cm
Formula
P = 3s
Calculate
P = 18 cm
Step 1: Write the perimeter formula for an equilateral triangle

For an equilateral triangle: Perimeter = 3 × side length

P = 3s

Step 2: Substitute the side length

P = 3(6)

Step 3: Calculate

P = 18

Step 4: Include unit

The perimeter is 18 cm.

Perimeter = 18 cm
Final answer:

The perimeter of the equilateral triangle is 18 cm.

Applied rules:

• Equilateral triangle perimeter: P = 3s

• All sides equal: In an equilateral triangle, all three sides are the same length

• Multiplication: Multiply side length by 3

Regular Polygon Perimeter Formulas
Rectangle
P = 2(l + w)
Two lengths, two widths
Square
P = 4s
Four equal sides
Triangle
P = 3s
Three equal sides
Pentagon
P = 5s
Five equal sides
Hexagon
P = 6s
Six equal sides
Octagon
P = 8s
Eight equal sides
Triangle
P = 3s
3 sides
Square
P = 4s
4 sides
Pentagon
P = 5s
5 sides
Hexagon
P = 6s
6 sides
Heptagon
P = 7s
7 sides
Octagon
P = 8s
8 sides
General Formula: P = n × s
Where n = number of sides, s = side length
Rectangle
P = 2(l + w)
Opposite sides equal
Square
P = 4s
All sides equal
Triangle
P = 3s
Equilateral triangle
Any Regular Polygon
P = n × s
n = number of sides
Universal Method for Regular Polygons:
  1. Count the sides: Determine how many sides the polygon has
  2. Identify side length: Find the length of each equal side
  3. Apply the formula: P = number of sides × side length
  4. Calculate: Multiply the number of sides by the side length
  5. Include unit: Add the unit (cm, m, inches, etc.)
Advanced Regular Polygon Exercises
4 Pentagon perimeter
Exercise 4
A regular pentagon has sides of 5 cm. What is its perimeter?
Definition:

Regular Pentagon: A 5-sided shape with all sides equal. P = 5 × side length

Given
side = 5 cm
Formula
P = 5s
Calculate
P = 25 cm
Step 1: Write the perimeter formula for a regular pentagon

For a regular pentagon: Perimeter = 5 × side length

P = 5s

Step 2: Substitute the side length

P = 5(5)

Step 3: Calculate

P = 25

Step 4: Include unit

The perimeter is 25 cm.

Perimeter = 25 cm
Final answer:

The perimeter of the pentagon is 25 cm.

5 Hexagon perimeter
Exercise 5
A regular hexagon has sides of 6 cm. What is its perimeter?
Definition:

Regular Hexagon: A 6-sided shape with all sides equal. P = 6 × side length

Given
side = 6 cm
Formula
P = 6s
Calculate
P = 36 cm
Step 1: Write the perimeter formula for a regular hexagon

For a regular hexagon: Perimeter = 6 × side length

P = 6s

Step 2: Substitute the side length

P = 6(6)

Step 3: Calculate

P = 36

Step 4: Include unit

The perimeter is 36 cm.

Perimeter = 36 cm
Final answer:

The perimeter of the hexagon is 36 cm.

Complete Summary: Perimeter of Regular Polygon Formula

Key Concepts and Definitions:

Perimeter: The total distance around the outside of a 2D shape. It's like walking all the way around the edge of the shape.

Regular Polygon: A polygon where all sides and angles are equal. Examples: equilateral triangle, square, regular pentagon, regular hexagon.

Irregular Polygon: A polygon where sides and/or angles are not all equal.

Rectangle: A 4-sided shape where opposite sides are equal and all angles are 90°.

Square: A special rectangle where all 4 sides are equal.

Equilateral Triangle: A triangle where all 3 sides are equal.

Core Rules and Principles:

• Perimeter Rule: Perimeter = sum of all side lengths

• Regular Polygon Rule: P = number of sides × side length

• Rectangle Rule: P = 2(length + width)

• Square Rule: P = 4 × side length

• Equilateral Triangle Rule: P = 3 × side length

Step-by-Step Method for Regular Polygons:
  1. Count the sides: Determine how many sides the polygon has (n)
  2. Measure or get side length: Find the length of each side (s)
  3. Apply the formula: P = n × s
  4. Calculate: Multiply the number of sides by the side length
  5. Include the unit: Add the unit of measurement (cm, m, inches, etc.)
Perimeter Example: Square

Square with side = 5 cm

Step 1: Count sides → n = 4

Step 2: Side length → s = 5 cm

Step 3: P = n × s = 4 × 5 = 20 cm

Step 4: The perimeter is 20 cm

Perimeter Example: Regular Pentagon

Regular pentagon with side = 7 cm

Step 1: Count sides → n = 5

Step 2: Side length → s = 7 cm

Step 3: P = n × s = 5 × 7 = 35 cm

Step 4: The perimeter is 35 cm

Perimeter Example: Rectangle

Rectangle with length = 8 cm and width = 4 cm

Step 1: P = 2(l + w) = 2(8 + 4) = 2(12) = 24 cm

Step 2: The perimeter is 24 cm

Perimeter Example: Equilateral Triangle

Equilateral triangle with side = 6 cm

Step 1: P = 3s = 3(6) = 18 cm

Step 2: The perimeter is 18 cm

Memory Tip 1: "Perimeter" sounds like "fence-meter" - you measure the fence around a yard!
Memory Tip 2: For regular polygons: P = number of sides × side length.
Memory Tip 3: Square has 4 equal sides → P = 4s.
Common Mistake: Don't forget that rectangles have 2 lengths and 2 widths.
Common Mistake: Always include units in your answer (cm, m, inches, etc.)
Key Takeaways: 1) Regular polygons have all sides equal, 2) Use P = n × s, 3) Count sides carefully.
Real World Application: Useful for measuring fences, borders, frames, and edges of objects.
Regular Polygon Formula Reference
P = n × s
Universal Regular Polygon Formula
Where: n = number of sides, s = side length
Formula Components
Regular Polygon Formulas:

Triangle (n=3): P = 3s

Square (n=4): P = 4s

Pentagon (n=5): P = 5s

Hexagon (n=6): P = 6s

Heptagon (n=7): P = 7s

Octagon (n=8): P = 8s

Special Cases:

Rectangle: P = 2(l + w) (not regular, but common)

Square: P = 4s (regular quadrilateral)

Complete methodology:
  1. Identify the polygon: Count the number of sides
  2. Check if regular: Verify all sides are equal
  3. Apply the formula: P = n × s
  4. Substitute values: Fill in the number of sides and side length
  5. Calculate: Multiply to get the perimeter
Tip 1: Always count the sides carefully to determine n.
Tip 2: Verify that all sides are equal before using the regular polygon formula.
Tip 3: For irregular polygons, add all side lengths individually.
Tip 4: Always check your answer by counting sides and multiplying again.
Common errors: Miscounting sides, using regular formula for irregular polygons, arithmetic mistakes.
Key formulas: Regular: P=n×s, Rectangle: P=2(l+w), Square: P=4s
Essential rules to remember:

• Regular polygon rule: P = number of sides × side length

• Rectangle rule: P = 2(length + width)

• Square rule: P = 4 × side length

• General rule: P = sum of all side lengths

• Unit rule: Always include the unit (cm, m, inches, etc.)

Examples: P=5(6)=30, P=4(7)=28, P=2(5+3)=16
Formula Applications

Questions & Answers

Question: I'm confused about why we multiply by 2 in the rectangle perimeter formula. Why isn't it just length + width?

Answer: Great question! When we calculate perimeter, we need to count ALL the sides of the rectangle. A rectangle has 4 sides:

  • One length side
  • One width side
  • Another length side (opposite to the first)
  • Another width side (opposite to the first)

So we have: length + width + length + width = 2×length + 2×width = 2(length + width)

Think of walking around the rectangle - you travel the length twice and the width twice!

Example: If length = 5 and width = 3, the perimeter is 5+3+5+3 = 16, which equals 2(5+3) = 16.

Question: My child is struggling with the difference between perimeter and area. How can I help them understand?

Answer: Here's a helpful way to explain the difference:

  1. Perimeter: Think of it as building a fence around a yard - you measure the distance around the outside
  2. Area: Think of it as covering the floor with tiles - you measure the space inside

Use physical examples: If you have a rectangular piece of paper:

  • Perimeter = measure the tape needed to go around the edge
  • Area = count how many small squares fit inside

Perimeter is measured in units (cm, m), while area is measured in square units (cm², m²).

Question: Are there any memory tricks to remember the different perimeter formulas for various shapes?

Answer: Yes! Here are some effective memory tricks:

  • Rectangle: "Two lengths, two widths" → P = 2(l + w)
  • Square: "Four equal sides" → P = 4s
  • Triangle: "Three sides to add" → P = a + b + c
  • Regular Polygon: "Number of sides times side length" → P = n × s

Visual memory trick: Draw the shapes and write the number of sides next to each:
Rectangle (4 sides, opposite pairs equal)
Square (4 sides, all equal)
Triangle (3 sides)

Physical activity: Walk around the perimeter of different shaped objects while counting the sides out loud.